What is the difference between docker-compose up and docker-compose start?

Whenever I execute

docker-compose start 
docker-compose ps

I see my containers with the state "UP". If I do

docker-compose up -d

I will see more verbose but it will have the same state. Is there any difference between both commands?

docker-compose start
(https://docs.docker.com/compose/reference/start/)

> Starts existing containers for a service.

docker-compose up
(https://docs.docker.com/compose/reference/up/)

> Builds, (re)creates, starts, and attaches to containers for a service. > > Unless they are already running, this command also starts any linked services. > > The docker-compose up command aggregates the output of each container > (essentially running docker-compose logs -f). When the command exits, > all containers are stopped. Running docker-compose up -d starts the > containers in the background and leaves them running. > > If there are existing containers for a service, and the service’s > configuration or image was changed after the container’s creation, > docker-compose up picks up the changes by stopping and recreating the > containers (preserving mounted volumes). To prevent Compose from > picking up changes, use the --no-recreate flag.

For the complete CLI reference:
https://docs.docker.com/compose/reference/

In docker Frequently asked questions this is explained very clearly:

> What’s the difference between up, run, and start? > > Typically, you want docker-compose up. Use up to start or restart > all the services defined in a docker-compose.yml. In the default > “attached” mode, you see all the logs from all the containers. In > “detached” mode (-d), Compose exits after starting the containers, but > the containers continue to run in the background. > > The docker-compose run command is for running “one-off” or “adhoc” > tasks. It requires the service name you want to run and only starts > containers for services that the running service depends on. Use run > to run tests or perform an administrative task such as removing or > adding data to a data volume container. The run command acts like > docker run -ti in that it opens an interactive terminal to the > container and returns an exit status matching the exit status of the > process in the container. > > The docker-compose start command is useful only to restart containers > that were previously created, but were stopped. It never creates new > containers.